Discussion Forum

1)

 Two identical glass rod S₁ and S₂ (refractive index=1.5)  have one convex end of radius of curvature 10 cm. They are placed with the curved surfaces at a distance d as shown in figure, with their axes (shown by the dashed line)  aligned. When a point source of light P is placed inside rod S₁ on its axis at a distance of 50 cm from the curved face, the light rays emanating from it are found to be parallel to the axis inside S₂. The distance d is 

Answer:

Option B

Explanation:

R=10cm

       Applying   $\frac{\mu_{2}}{v}-\frac{\mu_{1}}{u}=\frac{\mu_{2}-\mu_{1}}{R}$  two

 times

                             $\frac{1}{v}-\frac{1.5}{-50}=\frac{1-1.5}{-10}$

                              $\frac{1}{v}+\frac{1.5}{50}=\frac{0.5}{10}$

                                    $\frac{1}{v}=\frac{0.5}{10}-\frac{1.5}{50}$

                                                   $=\frac{2.5-1.5}{50}$

  $\Rightarrow$                                               v=50

                                               MN=d ,  MI₁  =50 cm,

                          NI₁     =(d-50) cm

 

Again,       $=\frac{1.5}{\infty}-\frac{1}{-(d-50)}=\frac{1.5-1}{10}$

               $\frac{1}{d-50}=\frac{1}{20}$

      d=70